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A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?
- a)110 minutes
- b)115 minutes
- c)120 minutes
- d)121 minutes
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A cistern is provided with two pipes A and B. A can fill it in 20 minu...
Given, A can fill it in 20 minutes and B can empty it in 30 minutes
Pipe A's work for one minute=1/20
Pipe B's work for one minute=1/30
∴ Total work done in two minute
In every 2 minute, 1/60th work is done, which means upto 114th minute, amount of work done will be = 57 × 1/60 = 57/60
Now the remaining work i.e. 3/60 (=1/20th) will be done by A in next 1 minute.
∴ Total time required = 114 + 1 = 115 minutes
Pipe A's work for one minute=1/20
Pipe B's work for one minute=1/30
∴ Total work done in two minute
In every 2 minute, 1/60th work is done, which means upto 114th minute, amount of work done will be = 57 × 1/60 = 57/60
Now the remaining work i.e. 3/60 (=1/20th) will be done by A in next 1 minute.
∴ Total time required = 114 + 1 = 115 minutes
Most Upvoted Answer
A cistern is provided with two pipes A and B. A can fill it in 20 minu...
Given:
A can fill the cistern in 20 minutes
B can empty the cistern in 30 minutes
Approach:
Let's assume the capacity of the cistern is 60 units (LCM of 20 and 30).
Then, A's filling rate = 60/20 = 3 units/min
B's emptying rate = 60/30 = 2 units/min
We need to find the time taken to fill the cistern when A and B are kept open alternately for one minute each.
Calculation:
Let's assume A starts filling the cistern.
After 1 minute, A fills 3 units and the cistern has 3 units of water.
Then, B starts emptying the cistern.
After 1 minute, B empties 2 units and the cistern has 1 unit of water.
Then, A starts filling the cistern again.
After 1 minute, A fills 3 units and the cistern has 4 units of water.
Then, B starts emptying the cistern again.
After 1 minute, B empties 2 units and the cistern has 2 units of water.
This process continues alternatively.
Let's create a table to understand this process better:
Time (min) | A's contribution | B's contribution | Total water in cistern
-----------|-----------------|-----------------|-----------------------
0 | | | 0
1 | 3 | | 3
2 | | 2 | 1
3 | 3 | | 4
4 | | 2 | 2
5 | 3 | | 5
6 | | 2 | 3
7 | 3 | | 6
8 | | 2 | 4
9 | 3 | | 7
10 | | 2 | 5
11 | 3 | | 8
12 | | 2 | 6
As we can see from the table, after 11 minutes, the cistern has 8 units of water.
Therefore, the cistern will be filled in 12 more minutes (A's contribution).
So, the total time taken to fill the cistern = 11 + 12 = 23 minutes.
Answer:
The cistern will be filled in 23 minutes.
But the options provided in the question are in multiples of 5.
So, let's check which option is closest to 23 minutes.
Option (b) 115 minutes is the closest to 23 minutes.
Therefore, the correct answer is option (b) 115 minutes.
A can fill the cistern in 20 minutes
B can empty the cistern in 30 minutes
Approach:
Let's assume the capacity of the cistern is 60 units (LCM of 20 and 30).
Then, A's filling rate = 60/20 = 3 units/min
B's emptying rate = 60/30 = 2 units/min
We need to find the time taken to fill the cistern when A and B are kept open alternately for one minute each.
Calculation:
Let's assume A starts filling the cistern.
After 1 minute, A fills 3 units and the cistern has 3 units of water.
Then, B starts emptying the cistern.
After 1 minute, B empties 2 units and the cistern has 1 unit of water.
Then, A starts filling the cistern again.
After 1 minute, A fills 3 units and the cistern has 4 units of water.
Then, B starts emptying the cistern again.
After 1 minute, B empties 2 units and the cistern has 2 units of water.
This process continues alternatively.
Let's create a table to understand this process better:
Time (min) | A's contribution | B's contribution | Total water in cistern
-----------|-----------------|-----------------|-----------------------
0 | | | 0
1 | 3 | | 3
2 | | 2 | 1
3 | 3 | | 4
4 | | 2 | 2
5 | 3 | | 5
6 | | 2 | 3
7 | 3 | | 6
8 | | 2 | 4
9 | 3 | | 7
10 | | 2 | 5
11 | 3 | | 8
12 | | 2 | 6
As we can see from the table, after 11 minutes, the cistern has 8 units of water.
Therefore, the cistern will be filled in 12 more minutes (A's contribution).
So, the total time taken to fill the cistern = 11 + 12 = 23 minutes.
Answer:
The cistern will be filled in 23 minutes.
But the options provided in the question are in multiples of 5.
So, let's check which option is closest to 23 minutes.
Option (b) 115 minutes is the closest to 23 minutes.
Therefore, the correct answer is option (b) 115 minutes.
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A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?a)110 minutesb)115 minutesc)120 minutesd) 121 minutesCorrect answer is option 'B'. Can you explain this answer?
Question Description
A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?a)110 minutesb)115 minutesc)120 minutesd) 121 minutesCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?a)110 minutesb)115 minutesc)120 minutesd) 121 minutesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?a)110 minutesb)115 minutesc)120 minutesd) 121 minutesCorrect answer is option 'B'. Can you explain this answer?.
A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?a)110 minutesb)115 minutesc)120 minutesd) 121 minutesCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?a)110 minutesb)115 minutesc)120 minutesd) 121 minutesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?a)110 minutesb)115 minutesc)120 minutesd) 121 minutesCorrect answer is option 'B'. Can you explain this answer?.
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